A289972 Number of sets S (cubic acute n-set), with cardinality A089676(n) >= 3, of points in {0,1}^n in real n-dimensional Euclidean space such that every angle determined by three distinct points in S is acute.

0, 0, 2, 16, 352, 240, 107520, 1032837120

Offset

1,3

Comments

Consider the 2^n points {0,1}^n in real Euclidean space. Then A089676(n) = maximal size of a subset S of these 2^n points such that there is no triple of points P,Q,R in S which subtends a right angle. That is, we are not allowed to have P-Q perpendicular to R-Q. Here we count such sets.

Links

Table of n, a(n) for n=1..8.

D. Bevan, Sets of Points Determining Only Acute Angles and Some Related Coloring Problems, Electronic J. of Combinatorics, 13(1), 2006, #R12.

Fausto A. C. Cariboni, Complete solutions for a(3)-a(6)

Fausto A. C. Cariboni, Complete solutions for a(7)

Crossrefs

Cf. A089676.

Sequence in context: A012610 A012721 A297095 * A179472 A009341 A366396

Adjacent sequences: A289969 A289970 A289971 * A289973 A289974 A289975

Keyword

nonn,hard,more

Author

Fausto A. C. Cariboni, Jul 16 2017

Status

approved